Question

calculate sigma and z effective for 4s and 3d electron of copper

Answer 1

electrons in lower groups

Step 3: Slater's Rules is now broken into two cases:

the shielding experienced by an s- or p- electron,

electrons within same group shield 0.35, except the 1s which shield 0.30

electrons within the n-1 group shield 0.85

electrons within the n-2 or lower groups shield 1.00

the shielding experienced by nd or nf valence electrons

electrons within same group shield 0.35

electrons within the lower groups shield 1.00

These rules are summarized in Figure 2.6.12.6.1 and Table 2.6.12.6.1.



Figure 2.6.12.6.1: Graphical depiction of Slater's rules with shielding constants indicated.

Shielding happens when electrons in lower valence shells (or the same valence shell) provide a repulsive force to valence electrons, thereby "negating" some of the attractive force from the positive nucleus. Electrons really close to the atom (n-2 or lower) pretty much just look like protons, so they completely negate. As electrons get closer to the electron of interest, some more complex interactions happen that reduce this shielding. T

Table 2.6.12.6.1: Slater's Rules for calculating shieldings[1s]0.30---[ns,np]0.35-0.851[nd] or [nf]0.35111

The shielding numbers in Table 2.6.12.6.1 were derived semi-empirically (i.e., derived from experiments) as opposed to theoretical calculations. This is because quantum mechanics makes calculating shielding effects quite difficult, which is outside the scope of this Module.

Calculating S

Sum together the contributions as described in the appropriate rule above to obtain an estimate of the shielding constant, S, which is found by totaling the screening by all electrons except the one in question.

S=∑niSi(2.6.1)(2.6.1)S=∑niSi

where

nini is the number of electrons in a specific shell and subshell and

SiSi is the shielding of the electrions subject to Slater's rules

EXAMPLE 2.6.12.6.1: THE SHIELDING OF 3P ELECTRONS OF NITROGEN ATOMS

What is the shielding constant experienced by a 2p electron in the nitrogen atom?

Given: Nitrogen (N)

Asked for: S, the shielding constant, for a 2pelectron

Strategy:

Determine the electron configuration of nitrogen, then write it in the appropriate form.

Use the appropriate Slater Rule to calculate the shielding constant for the electron.

Solution A  N: 1s2 2s2 2p3 

 N: (1s2)(2s2,2p3)

Solution B  S[2p] = 1.00(0) + 0.85(2) + 0.35(4) = 3.10

EXERCISE 2.6.12.6.1: THE SHIELDING OF VALENCE P ELECTRONS OF BROMINE ATOMS

What is the shielding constant experienced by a valence p-electron in the bromine atom?

Answer

EXAMPLE 2.6.22.6.2: THE SHIELDING OF 3D ELECTRONS OF BROMINE ATOMS

What is the shielding constant experienced by a 3d electron in the bromine atom?

Given: Bromine (Br)

Asked for: S, the shielding constant, for a 3delectron

Strategy:

Determine the electron configuration of bromine, then write it in the appropriate form.

Use the appropriate Slater Rule to calculate the shielding constant for the electron.

Solution A  Br: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5

Br: (1s2)(2s2,2p6)(3s2,3p6)(3d10)(4s2,4p5)

Ignore the group to the right of the 3d electrons. These do not contribute to the shielding constant.

Solution B  S[3d] = 1.00(18) + 0.35(9) = 21.15

EXERCISE 2.6.22.6.2: THE SHIELDING OF 3D ELECTRONS OF COPPER ATOMS

What is the shielding constant experienced by a valence d-electron in the copper atom?

Answer

Calculating Zeff

One set of estimates for the effective nuclear charge (ZeffZeff) was presented in Figure 2.5.1. Previously, we described ZeffZeff as being less than the actual nuclear charge (ZZ) because of the repulsive interaction between core and valence electrons. We can quantitatively represent this difference between ZZand ZeffZeff as follows:

S=Z−Zeff(2.6.2)(2.6.2)S=Z−Zeff

Rearranging this formula to solve for ZeffZeff we obtain:

Zeff=Z−S(2.6.3)(2.6.3)Zeff=Z−S

We can then substitute the shielding constant obtained using Equation 2.6.32.6.3 to calculate an estimate of ZeffZeff for the corresponding atomic electron.

EXAMPLE 2.6.32.6.3: THE EFFECTIVE CHARGE OF P ELECTRONS OF BORON ATOMS

What is the effective nuclear charge experienced by a valence p- electron in boron?

Given: Boron (B)

Asked for: ZeffZeff for a valence p- electron

Strategy:

Determine the electron configuration of boron and identify the electron of interest.

Use the appropriate Slater Rule to calculate the shielding constant for the electron.

Use the Periodic Table to determine the actual nuclear charge for boron.

Determine the effective nuclear constant.

Solution:

A B: 1s2 2s2 2p1 . The valence p- electron in boron resides in the 2p subshell.

B: (1s2)(2s2,2p1)

B S[2p] = 1.00(0) + 0.85(2) + 0.35(2) = 2.40

C Z = 5

D Using Equation 2.6.32.6.3, Zeff=2.60Zeff=2.60





Hope I'll help uuu